Travelling lightly and almost anywhere I can go.
Rome: Hostel/Hotel Suggestions?
I would say choose something on AirBnB and share the money for the rent. For the price you decide to pay you will get a better return for your money in terms of comforts than a hotel room.
Italy: North or South?
It depends on what time of year the trip will be but this is a very tricky question. If you pick the south then you will miss on Tuscany which is arguably the most beautiful area in Italy where you can see many of the renaissance masterpieces of Michelangelo...